Vibration damped turbo machinery



April 27, 1965 A. J. MILLER VIBRATION DAMPED TURBO MACHINERY Original Filed April 20. 1961 BOHIHdWV INVENTOR.

ARTHUR J. MILLER ATTORNEY.

United States Patent 3,180,616 VEBRATIUN DAMPER) TUREO MACHENERY thur J. Miller, Irwin, Pa, assignor to Carrier Corporation, Syracuse, N.Y., a corporation of Delaware Original application Apr. 20, 1961, Ser. No. 104,282, now

Patent No. 3,131,461, dated May 5, 1964. Divided and this application Jan. 3, 1964, er. No. 343,431

3 Claims. (Cl. 253-77) This application is a division of co-pending application,

Serial No. 104,282, filed April 20, 1961, for Vibration Damped Turbo- Machinery, now Patent No. 3,131,461, granted May 5, 1964. This invention relates broadly to bladed turbo machinery including steam turbines, gas turbines, axial and centrifugal flow compressors, fans and propellers. More particularly, this invention relates to an improved lashing construction for damping blade vibrations in turbo machinery and to an improved method of making a turbo machine of the vibration damped blade type.

Turbo machinery of the type contemplated by this invention, employs a plurality of radial blades which are secured to a rotor shaft. The turbo machine may be either of the type in which the energy of a fluid is transmitted to the blades for producing rotation of the shaft, such as a steam turbine, or it may be of the type in which the energy of the rotation of the shaft is transmitted to a fluid for producing movement or compression of the fluid medium such as an axial flow compressor.

Turbo machines in general are beset with a common difficulty which tends to undesirably limit the choice of design parameters. Due to the fact that the blades of a turbo machine are frequently long, thin members secured to a shaft at one end, the blades tend to vibrate during operation of the machine. irregularities in the distribution and flow of fluids in the machine may cause the blades to vibrate excessively at either their natural frequency or at a harmonic thereof. While the blades are frequently designed so as to avoid excessive vibration at their natural frequency in normal operation of the machine, it is often diificult or impossible to avoid vibrations at a harmonic frequency particularly where the turbo machine must be used at different or varying rotational speeds as during startup or slowdown of the machine. Vibration of the blades is a frequent cause of blade failure due to bending stresses in the blades caused by vibration of the blades. When the bending stresses exceed the maximum working stress of the blade material, a crack may develop at a blade edge. As the crack enlarges under further stress, a point is soon reached where the entire blade fractures and a substantial portion of the blade is loose in the machine and free to damage the other blades of the machine. Since machines of the type described frequently rotate at a very high speed, it has been observed that in some instances a broken blade has sufficient energy to crack the outer casing of the machine and be propelled completely through it.

To avoid the difliculty described, it is common practice to damp vibration of the blades of a turbo machine at its fundamental and some of its harmonic frequencies by lashing the blades together. Prior art lashings have taken many forms, but generally they have proved unsatisfactory for a number of reasons. For example, if all of the blades of a turbo machine are lashed together by a single ring of metal secured to each of the blades and lying in a single plane, the lashing member itself will often fail due to the enlargement of the blade diameter because of centrifugal forces and because of thermal expansion of the blades. The enlargement of the blade diameter imposes a tensil or hoop stress on the lashing member which often results in its failure. A frequent alternative, therefore, is to lash only a small group of blades together with a single lashing member. While this solution reduces the hoop stress in the lashing member, it fails to completely damp vibration of the blades and it introduces a new resonant vibration frequency which corresponds to natural period of vibration of the group of lashed blades. Also, this alternative sacrifices the desirable rigidity of constructions wherein all of the blades are lashed to their adjacent blades.

Other vibration damping schemes have been employed which utilize either partially loose lashing wires or rigid studs between the blades, but all of these schemes possess disadvantages which tend to limit their use in practical applications. For example, schemes requiring welding a lashing to the blades tend to structurally weaken the blades thereby making them more prone to failure. Furthermore, schemes which involve lashing which lies in only one plane fail to effectively damp transverse vibrations of the blades.

Moreover, the hoop stresses created by thermal and centrifugal expansion of the turbine blades are not the only cause of failure of prior art lashings. Because of the high speeds generally encountered in turbo machinery, the centrifugal forces imposed on the lashing frequently assume significant proportions and result in stresses which are directly superimposed on the hoop stresses previously described. The combination of these stresses tends to produce failure of the lashing and consequently the blades of the turbo machine are enabled to vibrate in destructive modes after failure of the lashing.

Furthermore, prior art lashing constructions have been generally confined to a single plane and, therefore, they failed to damp torsional modes of vibration which are characteristically present in turbine blades. Not only are the torsional modes of vibration a possible source of blade failure, but twisting of the blades due to centrifugal and thermal elfects tends to cause the blades to depart from their proper shape and impair efiicient operation of the turbo machine.

Accordingly, it is an object of this invention to provide an improved vibration damped turbo machine.

It is a further object of this invention to provide an improved method of making a vibration damped turbo machine.

These and other objects of this invention are achieved in the illustrated embodiment by lashing the blades of a turbo machine about a predetermined diameter by means of headed pins loosely inserted through apertures in the blades. A pin extends from the leading region of one blade to the trailing region of the other blade and this type of lashing is repeated about the entire fan wheel of the turbo machine. Consequently, each blade is lashed to its two adjacent blades in a rigid manner by a pin under tension and untwisting of the blades under the influence of thermal and inertial forces is restrained but high hoop stresses in the lashing are prevented.

A turbo machine in accordance with this invention may be made by forming a plurality of turbine blades each having apertures in their leading and trailing regions. Head bushings are formed having a shoulder thereon similar to the faces of the turbine blades adjacent which they are to be positioned. Lashing pins are inserted through the aperture in the leading region of one blade and through the aperture in the trailing region of the next adjacent blade. The head bushings are insented through the respective apertures in the blades and positioned so that their shoulders conform to the faces of the blades. The head bushings are secured. to the lashing pins. 1

The construction of a preferred embodiment of this invention will become more apparent by reference to the specification and attached drawing wherein:

FIGURE 1 is a partial front view of a turbo machine embodying this invention;

FIGURE 2 is a developed plan view of a lashing in accordance with this invention;

FIGURE 3 is a cross-sectional view of a head bushing which forms a part of the turbine lashing shown in FIGURE 2;

FIGURE 4 is a typical graph of the vibration amplitude of a conventionally lashed turbine blade; and

FIGURE 5 is a typical graph of the vibration amplitude of a turbine blade lashed in accordance with this invention.

Referring particularly to FIGURE 1, there is shown a portion or stage of the rotor member of a turbo machine. It will be appreciated that the terms turbine and turbo machine as they are used throughout this specification and claims are intended to be interpreted in a broad sense and to be generic to steam and gas turbines, turbochargers, axial and centrifugal fiow compressors, fans, propellers and other rotating 0r nonrotating bladed fluid machinery, all of which may embody the principles of this invention.

A plurality of turbine blades 12 are secured to rotor shaft 11 by means of Christmas tree joints 13 to form a rotor stage. It will be understood that blade is meant to be broadly construed to include blade-like protrusions such as compressor vanes or turbine blades. seen in FIGURE 2, blades 12 have a front or reaction face 14 and a rear face 15. If the turbine wheel rotates in the direction shown by the arrow in FIGURE 2, region 16 comprising the leading half of the blades may be designated as the leading region and region 17 comprising the trailing half of the blade may be designated as the trailing region. It will be noted that an aperture 18 of predetermined size and shape is formed in the leading region of each blade and an aperture 19 also of predetermined size and shape is formed in the trailing region of each blade.

Blades 12 may be formed with any desired shape which meets the structural requirements of the turbo machine. Generally, reaction face 14 is concave and rear face is convex when the blades are viewed in cross section. Blades of the type described are frequently used in a low pressure stage. of a steam turbine and are rela tively long having a substantial amount of twist about their longitudinal axis. For convenience of illustration, the twist of blades 12 has not been shown in FIGURE 2 but can be readily perceived from an examination of FIGURE 1. 7

Blades 12 are mounted on shaft 11 in spaced adjacency to one another. The blades can be said to be parallel to each other as mounted on the shaft, though it will be appreciated that because of their twist and curvature they generally do not lie in single planes. As mounted on the shaft, reaction face 14 of one blade and rear face 15 of the forward adjacent blade may be said to be remote tfaces because they are separated from each other by the thickness of their blades and the distance between their other or adjacent faces.

In the illustrated embodiment, the blades of the turbo machine are provided with optional lashing means 26 and a primary lashing means comprising pins as As best shown in FIGURE 1. Lashing means 26 is shown to be conventional inform and may comprise a plurality of wires each of which extends through. a group of five turbine blades l2 with'e-ach lashing wire secured to the center blade of the group by a weld 27. The primary lashingmeans comprising pins 25, is positioned to sub stantially damp the fundamental mode of vibration of blades 12 and the secondary lashing means such as Wire 26 may be positioned to damp a secondary mode of vibration of blades 12. If desired, secondary lashing means 25 may be modified or omitted, or additional lashing means may be employed to damp other desired modes of blade vibration. If only the primary lashing means is employed it will preferably be radially positioned to damp both primary and harmonic vibration modes.

Primary lashing means 25 comprises a plurality of pins which lie in separate planes. Each pin extends from the leading region lti-of one blade 12 to the trailing region 17 of the forward'adjacent blade. This type of lashing may continue around the entire circle of blades so that each blade is lashed to both of its adjacent blades- Consequently, 'a rigid turbo machine blade assembly is provided by this type of construction but one which is not liable to the creation of destructive hoop stresses in the lashing. Also, blade vibration in both the axial and transverse modes is effectively damped by this arrangement.

Lashing means 25 may comprise pin means having a rod 23 and a pair of head bushings 31 and 3'7 in the embodiment illustrated in the drawing to place the lash ing means under tension when the machine'is in use. Rod 28 may desirably be circular in cross section and solid in construction though other constructions and configurations may be. used. It is desirable to form rod 23 and head bushings 3i. and 37 from a high strength, high temperature alloy steel which is not subject to corrosion by the fluid to be passed through the turbo mach-inc.

Rod 28 extends through aperture 13 in the leading region of one blade and aperture 19 in the trailing region of the dorward adjacent blade. End Evil of rod 2% projects from the front or reaction face 1 of one blade and end 2% of the rod projects from the rear face 14 of the adjacent forward blade as shown in FIGURE 2. In other words, the ends of rod 23 project from the remote faces of adjacent turbine blades 12 of the turbo machine.

Pin 25 is provided with head bushings 31 and 37, one of which is illustratedin FIGURE 3. Head bushing 31 has a first exterior portion 33 of a predetermined shape and size so. that this portion of the head bushing will loosely slide through aperture 19 in the trailing region of its associated blade. First exterior portion 33 is desirably of substantially the same shape and size as the aperture in the trailing region of blade 12 through which it is to be inserted. Head bushing 31 has a second exterior portion 34 of larger dimension than first exterior portion 33. Shoulder means 32 is formed between first portion 33and second portion 34 and is of a size larger than the size of aperture 19 inthe turbine blade with which the head bushing is adapted to be used so that the head bushing will not pass completely through the apert-ure in the blade. Shoulder. 32 is formed with a shape which closely conforms to the shape of rear face 15 of the turbine blade through which the bushing is to be inserted. Head bushing 31 is also formed with an internal aperture 35 of substantially the same size and shape as the exterior configuration of end 29 of rod 28 with which the bushing is to be used so that'it may be telescoped over the end of the rod. First portion 33 of head bushing 31 makes an angle with shoulder 32 corresponding to the angle which will be formedbetweenrod 2S and rear face 15 of blade 12. It will be appreciated that lashing or pin means '25 may take a variety of other forms. Essentially, however, pin 25 comprises a pair of head means and means joining the'hea'd meansin the form described.

-The second head bushing 37 may be formed in a similar manner to head bushing 31 except that the shoulder 33 will conform with reaction face 14 of its associated turbine blade. It will be understood that if both ends of rod 28 are not of the same size or shape that second head bushing 37 will be appropriately constructed so as to telescope over the other end 30 of the rod. It will also be appreciated that head bushing 37 is formed with a first region which closely corresponds to the size and shape of aperture 18 in the leading region of the blade through which it is adapted to be inserted. As can be seen in FIGURE 2, when pin 25 is completed, shoulder 38 of head bushing 37 may face shoulder 32 of head bushing 31 to restrain outward movement of adjacent blades 12.

Head bushings 31 and 37 may be formed by any convenient process, it having been found that investment casting is readily adapted to the requirements of their manufacture. While in the illustrated embodiment two head bushings 31 anl 37 are shown to be formed separately from rod 28, it is entirely feasible to cast or otherwise form one of the head bushings integral with the end of its associated rod so that in constructing the turbine, only one head bushing need be secured to complete pin 25.

In making a turbo machine in accordance with this invention; blades 12 are formed with apertures 18 and 19 respectively in the leading and trailing regions thereof. While it is convenient to form blades 12 together with the necessary apertures therein by forging and thereafter finishing the blades, it is not necessary that apertures 18 and 19 be formed at the same time as blades 12. Blades 12 are then assembled on rotor 11 in spaced adjacency and secured thereto usually by welding or upsetting a portion of the metal of the rotor. Rod 28, which may initially be somewhat larger than the final pin length, is inserted through aperture 18 in the leading region of one of the blades and through aperture 19 in the trailing region of the adjacent forward blade. When properly positioned, end 29 of rod 28 projects slightly from rear face 15 of the adjacent blade and end 30 projectsslightly from reaction face 14 of the blade through which rod 28 is inserted. Head bushings 31 and 37 are then telescoped over the ends 29 and 30 respectively of rod 28. The head bushings are rotated, if necessary, so that the contour of their shoulders conform with the remote faces of blades 12 with which they are associated. Thereafter, the head bushings are secured to rod 28 by brazing, welding or other suitablemeans without, however, securing the head bushings to the blades. It is then desirable to grind off the end of the pins to match the contour of head of the bushings. A jig has been found convenient for holding the pin and the bushings prior to securing them together and as an assembly aid. It will be appreciated that if one of the head bushings is integral with or secured to rod 28 previous to its insertion through the apertures in blade 12., that it is only necessary to insert rod 28 in apertures 18 and 19 so that the head of the preassembled bushing conforms with the proper face of its turbine blade and then the other head bushing may be assembled to the other end of rod 28 as previously described.

An advantage of lashing a turbo machine in accordance with this invention will be observed by a comparison of FIGURES 4 and 5. In FIGURE 4, there is shown a typical graph of the vibration amplitude in a conventionally lashed turbo machine. It will be noted that the blade under analysis, vibrates with a relatively large amplitude due to the presence of harmonic frequencies of the fundamental mode of vibration of the blade. In contrast to this, FIGURE 5 shows a typical graph of the amplitude of blade vibration in a turbo machine constructed in accordance with this invention. It will be noted that in the latter case, vibration of the blade is held to a relatively small value.

One of the reasons for the significant reduction in the amplitude of vibration in a turbo machine made in accordance with this invention, lies in the fact that each of the turbine blades may be lashed to its two adjacent blades to form a complete hoop. Such a rigid construction is not feasible with a lashing means which lies in a single plane throughout the entire circle of the blade because of the hoop stresses and centrifugal forces which would be imposed on the lashing. However, the lashing of the instant invention does not lie in a single plane and consequently, destructive hoop stresses are avoided by a slight twisting of the blades of the machine. This construction, therefore, results in a desirably rigid lashing without the inherent disadvantages exhibited by prior art constructions.

In addition, the blades of a turbo machine tend to untwist under the influence of centrifugal force and thermal expansion. With conventional type lashings which lie in a single plane, the tendency of the blades to untwist is generally not inhibited. However, with the lashing of the instant invention, since motion of both ends of the blade about the blade axis is restricted the tendency of the blades to untwist is overcome. Furthermore, since pins 25 are loose in the corresponding apertures in blades 12 through which they are inserted the blades may assume a slightly greater twist when the turbo machine is cold or not in use. It will be seen that under these conditions, pins 25 are completely unstressed until the turbo machine is put into operation at which time the thermal and centrifugal eifects on the blades are sufiicient to untwist them to the point that their remote faces tightly abut the shoulders of the head bushings placing the lashing pins under tension. If the distance between the shoulders of the head bushings has been properly selected, the blades will have untwisted to an extent such that they have reached their desired position and aretight against the shoulders of the pins when the turbo machine has reached its operating speed and temperature. Further untwisting of the blades will be prevented even though the centrifugal forces or temperature rise would tend to produce this result because of the restraining actionof pins 25 once the blades have reached their desired condition. The designer, therefore, may choose a blade which is relatively thin and need not appreciably thicken the base of the blade in order to prevent the undesirable untwisting which has been described.

With the construction described, wherein the lashing pins are relatively short, the number of blades used in a particular turbine may be selected to give more nearly optimum fluid flow through the turbine than was possible with prior art constructions where the distance between the blades was an undesirably limiting factor in the design of an effective lashing. The use of fewer blades also results in cost savings and in improved etiiciency by reduction of frictional drag on the blades.

Another disadvantage in prior art constructions has been the necessity for heavily reinforcing the blades of a turbo machine in the region in which the lashing means is located. The relatively heavy reinforcement has added to the weight of the blade as well as forming an area of nonuniform surface on the blade which tended to disrupt fluid flow across the faces of theblades. However, with the improved construction described, it is possible to use a relatively slight reinforcement, if any, on the blade in the region of the lashing and consequently, a more uniform fluid flow is achieved.

Moreover, the improved lashing of the instant invention is effective to damp both tangential and torsional modes of vibration which further reduce the size and weight of the blades used since it has been previously necessary to comprise desired lightness for the fact of structural rigidity in order that torsional vibrations be reduced to a satisfactorily low level.

Likewise, because of the tendency of the blade to untwist under the influence of centrifugal forces imposed on it when rotating at high speed, the lashing pins are under tension in operation of the turbo machine. Consequently, tangential vibration of the blades is substan- (1 tially completely eliminated and blade failure is materially reduced. Also, failure of the lashing, which has been a serious problem in prior art constructions, is substantially reduced because the pin is placed in axial tension and is not subject to fatigue failure due to bending stresses which have characterized prior lashing constructions. This latter feature is highly advantageous because it is obvious that however effective a lashing construction may be in damping the various modes of blade vibration, such a construction is rendered useless if stresses are set up in the lashing which will tend to cause the lashing to fail in service. Prior art lashings have frequently damped blade vibration at the expense of bending stresses being set up in l The disadvanstresses imposed on it during operation of the machine and secondly, the heat from the welding operation tended to adversely affect the mechanical strength of the blade. For example, the welding process frequently caused air hardening of a turbine blade making this region more susceptible to fracture under the flexure produced by vibration of the blades. In the present construction, no mechanical connection is made to the blades and only a simple and easily controllable brazing operation is required to be performed in the area of the blade. quently, change in blade characteristic due to securing of the lashing means is negligible with the instant construction.

It can be seen, therefore, that the design of turbo machinery made in accordance with this invention is less restricted by the destructive nature of stress producing vibrations than has been true of prior constructions. Consequently, the application of the instant invention results in a more emcient turbo machine which may be lower in cost and more durable and reliable in operation than previous machines.

While there has been described a preferred embodiment of this invention, it will be understood that this invention is not limited by the form shown and described, but that various modifications and embodiments thereof may be constructed within the scope of the following claims;

I claim:

1. in a vibration damped turbo machine having a shaft,

(1) a first blade member having a pair of opposed faces and an aperture formed in a leading region thereof secured to said shaft;

(2) a second blade member having a pair of opposed faces and an aperture formed in a trailing region thereof secured to said shaft, said second blade being secured in spaced adjacency to said first blade on said shaft of said turbo machine;

(3) a lashing pin extending loosely through said apertures in said first and second blades, said lashing pin having (a) first head means secured to said pin adjacent the face of said one blade most remote from said second blade, and second head means secured to said pin adiacent the face of said sec- 0nd blade most remote from said first blade, said head means comprising shoulders larger than the respective apertures in the blades through which said lashing pin extends; and (b) at least a portion of said lashing pin extending inwardly from each of said shoulders which is of a smaller size than the respective adjacent apertures through which said pin extends, so that Cause I 8 said blades are restrained from moving away from each other more than a desired extent by said shoulders and maymove toward each other in sliding frictional engagement with said pin to damp blade vibrations in saidturbo machine.

2. A vibration damped turbo m'achine'having a rotor shaft and comprising: 7

(l) a plurality of radially extending, twisted, blades having a pair of opposed faces, saidblades being secured to said rotor shaft, each of said blades having an aperture formed in a leading region thereof and an aperture formed in a trailing region thereof; and

(2) said blades being lashed together by a series of lashing pins, each of said, lashing pins extending loosely through said aperture in the leading region of one of said blades and through said aperture in the the trailingregion of the next blade, said lashing pin being arranged so as tores train movement of said adjacent blades away from each other greater than a predetermined desired distance, and to allow movement of said blades towards each other by sliding in frictional engagement along said pin to damp vibrations in said turbo machine, each of said lashing pins comprising: 7

(a) a rod portionhaving a pair of ends,

(b) a head bushing secured to one endof said rod portion adjacent one of the faces of one or" the blades through which said lashing pin extends, said one face beingthat which is most remote from the other adjacent blade through which said lashing pin extends, said head bushing comprising:

(1) a shoulderportion of a size greater than the size of the aperture in said one blade through which said lashing pin extends,

(2) a portion extending througlrsaid aperture in said one blade and having an exterior size andshape so that'said bushing may be loosely inserted in said aperture,

(3) a portion telescopically engaged with, and

secured to, said rod portion, and

(c) said lashing pin further comprising head means secured to the other end'of saidrodmeans adjacent one of the faces of said other adjacent blade, said one face 'being that which is most 7 remote from said one blade. 7

3. Avibration damped turbo machine having a rotor shaft and comprising: 7

(1) a plurality of radially extending, twisted, blades having a pair of opposed faces, said blades being secured to said rotor shaft,each of said blades having an aperture formed in a leading region thereof and 'an aperture formed in a trailing region thereof; and

(2) said blades being lashed together by a series of lashing pins, eachofl said lashing pins extending loosely through said aperture in the leading region of one of said blades and through said aperture in the trailing regionofthe next blade, said lashing pin being arranged so as to restrain'movemcnt of said adjacent blades away from each other greater than a predetermined desired distance, and to allow movement of said. blades towards each other by sliding in frictional engagement along said pin to damp vibrations in said turbo machine, each of said lashing pins comprising; 7

(a) a rod portion having a pair of ends and being of a length greater than the distance between said apertures through which said lashing pin extends, V

(b) a head bushing secured to one end of said rod portion adjacent-one of the faces of one of the blades through which said lashing pin extends, said one face being that which is most 7 remote from the other adjacent blade through 9 which said lashing pin extends, said head bushing comprising:

(1) a shoulder portion of a size greater than the size of the aperture in said one blade through which said lashing pin extends,

(2) a portion extending through said aperture in said one blade and having an exterior size and shape so that said bushing may be loosely inserted in said aperture,

(3) an aperture in said head bushing into which said rod portion extends in telescopic engagement therewith, and

(c) said lashing pin further comprising head means secured to the other end of said rod means adjacent one of the faces of said other adjacent blade,

from said one blade.

References Cited by the Examiner UNITED STATES PATENTS 937,006 10/09 McKee 255 77 1,542,402 6/25 Meissner 253-77 1,618,285 2/27 Kasley 253-77 2,962,259 11/60 Bishop 253-47 FOREIGN PATENTS 244,518 12/25 Great Britain. 696,557 9/53 Great Britain.

15 KARL J. ALBRECHT, Primary Examiner. JOSEPH H. BRANSON, ]R., Examiner. 

1. IN A VIBRATION DAMPED TURBO MACHINE HAVING A SHAFT, (1) A FIRST BLADE MEMBER HAVING A PAIR OF OPPOSED FACES AND AN APERTURE FORMED IN A LEADING REGION THEREOF SECURED TO SAID SHAFT; (2) A SECOND BLADE MEMBER HAVING A PAIR OF OPPOSED FACES AND AN APERTURE FORMED IN A TRAILING REGION THEREOF SECURED TO SAID SHAFT, SAID SECOND BLADE BEING SECURED IN SPACED ADJACENCY TO SAID FIRST BLADE ON SAID SHAFT OF SAID TURBO MACHINE; (3) A LASHING PIN EXTENDING LOOSELY THROUGH SAID APERTURES IN SAID FIRST AND SECOND BLADES, SAID LASHING PIN HAVING (A) FIRST HEAD MEANS SECURED TO SAID PIN ADJACENT THE FACE OF SAID ONE BLADE MOST REMOTE FROM SAID SECOND BLADE, AND SECOND HEAD MEANS SESECURED TO SAID PIN ADJACENT THE FACE OF SAID SECOND BLADE MOST REMOTE FROM SAID FIRST BLADE, SAID HEAD MEANS COMPRISING SHOULDERS LARGER THAN THE RESPECTIVE APERTURES IN THE BLADES THROUGH WHICH SAID LASHING PIN EXTENDS; AND (B) AT LEAST A PORTION OF SAID LASHING PIN EXTENDING INWARDLY FROM EACH OF SAID SHOULDERS WHICH IS A SMALLER SIZE THAN THE RESPECTIVE ADJACENT APERTURES THROUGH WHICH SAID PIN EXTENDS, SO THAT SAID BLADES ARE RESTRAINED FROM MOVING AWAY FROM EACH OTHER MORE THAN A DESIRE EXTENT BY SAID SHOULDERS AND MAY MOVE TOWARD EACH OTHER IN SLIDING, FRICTIONAL ENGAGEMENT WITH SAID PIN TO DAMP BLADE VIBRATIONS IN SAID TURBO MACHINE. 